Most video tapes work using helical scanning for the video signal, recording one field of video for each (diagonal) pass along the tape (see interlaced video info page), with a control track recorded along one edge of the tape (regulating tape speed, and the alignment between the tape position and the rotating head), and an audio track (or two) along the other edge of the tape. Some also record HiFi sound tracks using the helical drum, between the video tracks, with either an analogue FM or digital signal.
The helical scan is used (diagonally sweeping across the tape, many times per second), to achieve a very high tape speed past the recording/playback head without having to wind the tape at a fast rate (you'd need an incredibly long cassette to achieve that speed with stationary heads). The high speed is needed due to the amount of information being used for the video signal. A useful side effect of the spinning drum is that we can get “still”, or other “trick” playback effects, as the tape and head are always moving against each other, even when the tape is not moving through the cassette, and that most modern VCRs have a complete field recorded in each scan (older professional machines only recorded a few lines of video during each pass, so a “still” picture could only be a few lines out of the entire picture).
However, the mechanical nature of VCRs means that tape playback isn't very stable, it introduces timing errors into the playback. For the average VCR, playing to the average TV set, it's not too noticeable—though older sets would often flag weave at the top of the picture, and you can often hear the sound wavering. But for professional use (e.g. TV studios), where video signals are combined between tapes and cameras, this instability makes tape playback unusable. Time base correctors are used to remove the instability (the signal is fed in, and clocked out, at a standard rate, against a reference source), producing a stable, and standard, output. Even simple tape-to-tape dubbing benefits from using a stabilised source; as without it you've got one unstable mechanical system playing back a tape, and another unstable mechanical system trying to sync to the first one to record it (this effect gets worse with copies of copies). One immediately obvious effect of unstable video playback is wiggly edges to what should be vertical lines (e.g. seeing tall buildings with crinkled edges).
Tape damage doesn't just ruin a recording, but can also damage the machine playing it, and other tapes. For instance, spilling liquids onto a tape means that something will remain on the surface of the tape, and will end up contaminating the surfaces it touches inside the VCR, which will then contaminate the next tape that it plays. Likewise, with other contaminants.
For the best life of your tape, your VCR, and any other tape that will be used in it, you should look after all of your tapes.
Machines are notorious for chewing tapes, though they're more likely to do that during certain operations:
For those reasons, it's best to avoid doing those actions in the middle of recordings; and to leave some lead-in space at the start of new tapes (a spare portion that, if chewed, is before the part of the tape that you want to watch).
However, if while playing a tape you realise it's starting to chew it (because you can see, or hear, the effect), immediately stop and eject the tape, then look at it to see that it's wound into the shell properly before putting it back in and continuing to use it.
A few times I've had machines chew a tape when I've started them recording, and haven't found out until later that they've ruined the entire recording. Now, I always start a recording by threading up the tape, checking that it plays correct, then “pausing” the tape at the right point to record onto, and beginning recording from the paused mode (not from the “stop”, or an unthreaded, mode). Machines are unlikely to start chewing the tape while just coming off the pause mode as there's very little mechanical movement associated with that action.
Video tapes have a longer and better quality life when stored on edge (any of the thinner dimensions of the cassette or spool). When stored flat the edges of the tape can get crushed against the spool, and bent back; particularly when the tape has wound unevenly, with portions of the tape sticking out (even by tiny amounts).
During playback, damaged portions of the tape cause the tape to move out of the correct position, which not only means that playback isn't as good as possible, but further damage may occur.
Because several of my VCRs wind the tapes poorly during fast-forward and rewind, but do wind them neatly during playback, I usually don't rewind my tapes after watching them. This minimises any chance of further damage during storage and carrying them around, as the only parts of the tape that might stick out and get knocked are between programs (I avoid stopping and ejecting tapes in the middle of recordings).
Of course I have to rewind them to play them, and it doesn't do a great job, then; but they're not so likely to get knocked and damaged inside the VCR, as when sitting on the shelves, being jostled around looking for the right tape, being dropped, and carried around the house to whichever VCR is going to play them.
Sometimes when you're trying to play a tape that's been in a different machine (brand new tapes, borrowed tapes, or if you have more than one VCR) it may have wound it at a different tension, and may not playback, or playback very well. In these circumstances it can help to fast-forward then rewind through the tape, before trying to play it.
For storage purposes, it's better that tapes stand up on one of their thinner edges (any edge, it doesn't matter which). If you must leave tapes laying flat, then place them in the same way up as they go into the VCR. This means that the holes (where contaminants could get in) are under the cassette, not facing up just waiting to catch whatever falls in; and that the spools are resting flat against the bottom of the cassette, not balancing on the springs, floating about, and mangling the edges of the tape any time that they move.
Despite most video cassettes having covers over the tape, they don't “seal out” dust and other contaminants, they can still get in. Dirt can damage the tape in more than one way. It can chemically react with the tape, and deteriorate it. It coats the tape with an abrasive substance, which wears off the surface of the tape and the VCR's tape path. Keep tapes in their boxes when you're not using them, and store them the right way.
Video tapes are magnetic recordings, as such they can be erased by other magnetic fields. Though it (generally) takes a very strong, and close, field to do that. However, it's better to be cautious, and avoid storing tapes in various places.
Many tapes are NOT made of very stable materials, and can easily be ruined by environmental factors. Moisture can cause the tape to stick to itself and other things, coming apart when being played (being stripped), or getting stuck in position. Heat and plastics are a bad mix, plastic melts and changes shape easily, and can chemically react (notice how hot tapes smell worse than cold ones—that's some of the contents evaporating, never to be a part of that tape anymore).
It's recommended that tapes aclimitise to the same conditions as the machine that's going to play them for a long period (perhaps over an hour) before being used. For that reason, it's best to store tapes in the same room (or conditions) as the VCR.
From time to time I'm asked to repair a damaged tape. That really isn't possible, you can't splice broken tapes back together—the splice will come apart. You can't flatten out crinkled tapes; and you can't un-stretch stretched tapes. However, you can put a broken tape into two shells, discarding any mangled parts from the section between them. Splices between a tape and leader (which isn't dragged across the tape path) do work, as long as proper splicing tape is used, not ordinary sticky tape. Splices don't work in the middle of a tape (where it has to go around 180 degree bends, and over an expensive, spinning, video head drum).